Rinse flank steak and pat dry. In a 1-gallon zip-lock plastic bag or a large bowl, mix soy sauce, olive oil, brown sugar, green onions, sesame seeds, garlic, pepper, and ginger. Add steak, seal bag or cover bowl tightly, and chill, turning meat occasionally, at least 4 hours or up to 2 days.
Lift steak from marinade and let drain briefly. Place meat on a grill over a solid bed of medium-hot coals or medium-high heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds); close lid on gas grill. Cook steak, turning occasionally to brown evenly, until medium-rare (still pink in the center; cut to test), 9 to 12 minutes.
Transfer steak to a platter and let stand 10 minutes. Cut meat across the grain into thin, slanting slices.